Henry Ernest Dudeney/Modern Puzzles/132 - The Garden Bed/Solution

Modern Puzzles by Henry Ernest Dudeney: $132$

The Garden Bed

A man has a triangular lawn of the proportions shown,

and he wants to make the largest possible rectangular flower-bed without enclosing the tree.

Solution

From Largest Rectangle Contained in Triangle, the largest rectangle that can be inscribed within a triangle is situated such that:

Two of its vertices lie on one side of the triangle

Its other two vertices bisect the other two sides of the triangle.

This solution works only if the tree is sufficiently close to the corner that it is not enclosed inside at least one of those largest rectangles.

$\blacksquare$

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $132$. -- The Garden Bed
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $262$. The Garden Bed